Optimal Tracking Control for Discrete-time Systems with Time-delay Based on the Preview Control Method

Abstract In this paper, the optimal tracking control problem for discrete-time with state and input delays is studied based on the preview control method. First, a transformation is introduced. Thus, the system is transformed into a non-delayed system and the tracking problem of the time-delay system is transformed into the regulation problem of a non-delayed system via processing of the reference signal. Then, by applying the preview control theory, an augmented system for the non-delayed system is derived, and a controller with preview function is designed, assuming that the reference signal is previewable. Finally, the optimal control law of the augmented error system and the optimal control law of the original system are obtained by letting the preview length of the reference signal go to zero.